What is Pendulum: Definition and 1000 Discussions

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing.
From the first scientific investigations of the pendulum around 1602 by Galileo Galilei, the regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the 1930s. The pendulum clock invented by Christiaan Huygens in 1658 became the world's standard timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s. Pendulums are also used in scientific instruments such as accelerometers and seismometers. Historically they were used as gravimeters to measure the acceleration of gravity in geo-physical surveys, and even as a standard of length. The word "pendulum" is new Latin, from the Latin pendulus, meaning 'hanging'.

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  1. O

    Local Minimum of Potential Function of Spherical Pendulum

    Homework Statement http://img13.imageshack.us/img13/5793/84188411.jpg Homework Equations Find a condition on b such that x = 0 is a local minimum of the potential function. The Attempt at a Solution To find local minimum, potential function (V) of the system should be written. V...
  2. F

    Differential equation for motion of a pendulum

    Hello, I'm trying to create a model of pendulum motion in Matlab to fit the curve we measured in class, and it has some non-linear components (friction). It looks like the best fit is a sinusoid with an envelope given by a parabola (see attached file). The equations of motion are given by...
  3. H

    Simple Pendulum: Amplitude, velocity, and angular position.

    θθHomework Statement A simple pendulum of mass 20.0 g is suspended by a length of string 1.0 m. It is pulled from equilibrium so that it's raised 10.0 cm and released. Angular position given by θ(t)=θmaxcos(ωt+∅) What is the period? What is the maximum velocity of the pendulum? What is the...
  4. M

    Conical Pendulum Problem: Mass, Length, and Revolutions Per Minute

    Homework Statement A particle of mass 6 kg is attached to the centre B of a light inextensible string of length 10m. One end of the string is attached to a point A and the other end to a point C which is distance 8m directly below A. The particle is moving in a horizontal circle, with both...
  5. D

    Pendulum with two springs and a stick

    Homework Statement A pendulum consists of a stick of length L and mass M that is pivoted about its center, and attached to a pair of springs of stiffness k. As shown in attached pic, the springs are symmetric about the pivot, and the distance between them is l. a) Find the natural...
  6. Z

    What is the Correct Equation for Circular Motion with a Pendulum?

    Homework Statement Homework Equations Ac= V^2/R Theta is made by the upwards component of tension and tension itself. The Attempt at a Solution I know Sum of all forces = MA. Though for circular motion you always subtract the bigger number by the smaller one (bigger one being the force...
  7. R

    Is This a Physical Pendulum?

    I have to calculate the small oscillations around the equibrillum position. My question is only that is this a physics pendulum so i can use the formula T=2\pi\sqrt{\Theta/mgd} , where d is the distance of the mass centre and the pivot and \Theta is the moment of inertia of the pendulum about...
  8. C

    Why Is the Pendulum's Center of Mass Calculation Confusing?

    Homework Statement Why is the attachment true? (It's from my notes) Homework Equations General centre of mass equations The Attempt at a Solution Really not sure how the lecturer did this. It's quoted as if it's obvious but I don't see it at all, this has been annoying me for a...
  9. P

    Lagrangian of Pendulum: Calculation & Small Oscillations

    Homework Statement Consider a pendulum of mass m and length b in the gravitational field whose point of attachment moves horizontally x_0=A(t) where A(t) is a function of time. a) Find the Lagrangian equation of motion. b) Give the equation of motion in the case of small oscillations. What...
  10. K

    Transformations of Energy in a Pendulum Type Experiment

    Homework Statement The string in Fig. 8-35 is L = 120 cm long, has a ball attached to one end, and is fixed at its other end. The distance d to the fixed peg at point P is 75.0 cm. When the initially stationary ball is released with the string horizontal as shown, it will swing...
  11. S

    Moments & Pendulum: Different Lengths, Same Oscillation?

    if i have two forces acting at two different angles at a same spot will the addition of the moments of the two forces be the same as the moment whereby i take the net force of the two forces and get the moment of the net force of the same two forces? is there a way to explain why for the same...
  12. Z

    How Does Bullet Speed Change After Hitting a Pendulum?

    Homework Statement A 10g bullet moving at 300.m/s hits and passes through a 2.20kg pendulum target. After the impact, the 1.20m long pendulum rises up to an angle of 15 degree, find the final speed of the bullet. Homework Equations Ek= 1/2MV^2 Ep= MGH Momentum = MV The Attempt at a...
  13. D

    Angular frequency of a pendulum

    Homework Statement A physical pendulum consists of a small 1.5kg mass at the bottom end of a uniform 1.00m long 1.5kg stick swinging about its upper end. The moment of inertia of the pendulum about its upper end is 2.00kg*m^2. What is the angular frequencyHomework Equations sqrt(mgd/I)=w I...
  14. E

    Deriving 3D Newton-Euler Equations for Inverted Telescopic Pendulum Model

    Homework Statement I have to derive Newton euler equations of an inverted telescopic pendulum with two links. I will use this model to simulate biped walking. The leg link is assumed to be massless and it carries the body link. The model at final stage should be 3d. In 3d case the hip namely...
  15. A

    A pendulum impact hammer setting objects off on a frictionless surface.

    Hi,I want to design a crude pendulum impact device which i can use to measure initial velocities of objects on a frictionless surface. i.e measure energy at the start and end of the pendulums swing, to see how much has been absorbed into the impact. Heres my question about momentum on...
  16. L

    Angular momentum of ball spinning on a pendulum around a support point

    Homework Statement A ball (mass M: 0.250kg) is attached to a rope (length l: 1.69m) that is fixed to a point somewhere. The ball is spinning in a circle around the support point so that the rope makes an angle 37 degrees from the vertical. I have to find the magnitude of the angular momentum of...
  17. M

    How High Will Each Ball Swing After Elastic Collision?

    Urgent! Pendulum problem elastic collision Homework Statement An elastic ball (A) with mass m is released from a horizontal position, connected via a massless string to a rod. When the ball reaches the bottom, it collides with another elastic ball (B) of twice the mass, aslo connected...
  18. S

    Using Vector in Determining Period of Pendulum Inside a Moving Train

    Hi all, i have a question relating to the period of pendulum. I got this question: A bob of mass 0.5 kg is suspended by a string from the ceiling inside a train moving on a straight level rail (to the right). If the train has an acceleration of 0.2g, what is the tension in the string when the...
  19. N

    Determine the maximum tension in the pendulum rod

    Homework Statement A clock’s pendulum is 60 cm long with a bob at the end of mass 500 g. Determine the maximum tension in the pendulum rod when the bob is b) swinging at a speed of 2.4 m/s Homework Equations v^2 / r = ac The Attempt at a Solution 9.8m/s^2 = g (2.4)^2 / 0.6 = 9.6m/s^2...
  20. P

    Derivation of simple pendulum formula

    You pull a simple Pendulum of length 0.240 m to the side through an angle of 3.5 degrees and release it. (a) How much time does it take the pendulum bob to reach its highest speed? (b) How much time does it take if the pendulum is released at an angle 1.75 degrees instead of 3.5 degrees?
  21. I

    Elliptic Pendulum: Homework on Kinetic & Potential Energies

    Homework Statement A uniform rod AB of mass M and length 2l attatched to a slider at A which is constrained to move along a smooth horizontal wire. The rod, which is subject to gravity, is free to swing in the vertical plane containing the wire. Using Ω (the angle between rod and vertical)...
  22. A

    Pendulum with its pivot accelerating upward

    A pendulum of length, b, and bob with mass, m, is attached to a massless support moving vertically upward with constant acceleration a. Find the equation of motion. This problem is easy with the help of Lagrangian dynamics: bθ''+(g+a)θ=0 But how to solve this problem using Newton's...
  23. U

    Uniform Rod Pendulum - Lagrangian and Equations of Motion

    Homework Statement A uniform rod AB of mass M and length 2l attatched to a slider at A which is constrained to move along a smooth horizontal wire. The rod, which is subject to gravity, is free to swing in the vertical plane containing the wire. Using Ω (the angle between rod and vertical)...
  24. S

    Linearising compound pendulum equation

    Homework Statement Linearise T=2pi√(K^2 + h^2)/gh K is known constant This is a compound pendulum equation, I want to plot some kind of formula with variable T against some kind of formula with variable H in order to find g from the gradient. Homework Equations The Attempt at a...
  25. S

    Angle for SHM(Simple pendulum)

    Hi! Why it is necessary to has angle in radians for SHM(Simple pendulum)?
  26. L

    Quick Lagrangian of a pendulum question

    Homework Statement Use the E-L equation to calculate the period of oscillation of a simple pendulum of length l and bob mass m in the small angle approximation. Assume now that the pendulum support is accelerated in the vertical direction at a rate a, find the period of oscillation. For what...
  27. J

    Ballistic pendulum, finding final height

    Homework Statement The Attempt at a Solution I used conservation of momentum for the initial velocity of mass 2, and conservation of mechanical energy for the movement from rest to highest position, KE=PE. The answer that I received is selected in the screenshot. However, when the...
  28. S

    Pendulum Period change due to gravitational force change

    Hey, I was wondering how to go about a pendulum problem, basically if we have a clock pendulum that oscillates with period 2s unaffected; if we add a large mass on the floor, so that the pendulum experiences some small extra gravitational force towards the floor. Now I have determined this...
  29. Gh778

    Weight of the support of a pendulum with initial speed

    Hi, I'm interresting about the weight of the support of the pendulum with an initial speed. It is the http://en.wikipedia.org/wiki/Pendulum but with an initial speed. The mass come at top with straight initial speed and after turn around the pendulum. I attempt to have the weight of the...
  30. C

    Pendulum Damped by Air Resistance

    Homework Statement I need to develop an equation for the damping factor with respect to time for a pendulum that consists of a spherical mass attached to a string that is damped by air resistance. Homework Equations We are given that the curve fit for the drag coefficient is...
  31. L

    Determining Velocity of Ball Fired Horizontally from Ballistic Pendulum

    I am trying to determine the velocity of a ball fired horizontally from ballistic pendulum. The data is as follows: ball mass: 62.2 g spring mass: 14.7 g rod mass: 89.3 g length of spring: 126.1 mm initial spring length: 5 cm compressed spring length: 1 cm k: 2.05 N/m calculated from...
  32. F

    Magnetic Pendulum Mathematica Simulation

    Homework Statement This is for a lab, which I'm working on at home. There are two parts: using Mathematica to simulate a magnetic pendulum with 3 magnets by plotting the path of the bob and then extend my code to determine where the bob endpoint for all starting positions and draw the fractal...
  33. fluidistic

    Lagrange multipliers in a simple pendulum

    Homework Statement Not really a homework question, just want to check out if what I'm doing is right. I challenged myself to find the equation of motion and the forces in the simple pendulum system but with using the Lagrange multipliers and the constraint equation.Homework Equations In next...
  34. L

    MATLAB MATLAB problem with Kapitsa pendulum

    Homework Equations Theory for Kapitsa pendulum predicts that the motion consists of 2 parts: x(t)=X(t)+ x˜(t) (1) With fast oscillations: x˜(t)=−AX(t)sin(wt) /(w^2) (2) and a slowly varying motion X(t) which satisfies the following equation, X''=(1−(A^2)/(2w^2))X (3) Homework Statement 1...
  35. J

    Dynamics: max horizontal swing of a pendulum

    Homework Statement In an ore-mixing operation, a bucket full of ore is suspended from a traveling crane which moves along a stationary bridge. The crane is traveling at a speed of 3 m/s when it is brought to a sudden stop. Determine the maximum horizontal distance through which the bucket...
  36. R

    Find how much a wire stretched at the bottom of swing of pendulum

    1. A building is to be demolished by a 400kg shell ball swinging on the end of a 30.0 m steel wire of diameter 5.00 cm hanging from a tall crane. As the ball is swung though an arc from side to side, the wire makes an angle of 50° with the vertical at the top of the swing. find the amount by...
  37. T

    What are some potential experiments that can be designed using Kater's pendulum?

    Hi guys, Sorry if I've placed this on the wrong board. The blurb says the problems posted here should be math-based, but I wasn't sure of where else would be appropriate. Homework Statement I am tasked with designing an experiment for my second-year experimental physics class which...
  38. O

    Classical Mechanics: Lagrangian for pendulum with oscillating support

    Homework Statement Greetings! This is an example problem at the end of Chapter 1 in Mechanics (Landau): A simple pendulum of mass m whose point of support oscillates horizontally in the plane of motion of the pendulum according to the law x=acos(\gamma t) . Find the Lagrangian...
  39. D

    What is the Maximum Height of a Pendulum on the Right?

    Homework Statement A pendulum is released at A and caught by a peg as it passes through the vertical, B. To what height will the bob rise on the right?Homework Equations None givenThe Attempt at a Solution I really am unsure about how I am supposed to figure the height when no numbers were...
  40. M

    How Does Motion Impact Pendulum Clock Accuracy?

    Hey guys, I've been trying to find out about the expected effect of acceleration and/or motion on a pendulum clock; I asked this question in the mechancial engineering section of PF but didn't get any replies. It pertains to Einsteinian relativity also, specifically the effect of motion on...
  41. fluidistic

    Solving a Pendulum Problem Using the Lagrangian Approach

    Homework Statement A mass m is attached to one end of a light rod of length l. The other end of the rod is pivoted so that the rod can swing in a plane. The pivot rotates in the same plane at angular velocity \omega in a circle of radius R. Show that this "pendulum" behaves like a simple...
  42. T

    Angular Momentum (pendulum) Help

    Homework Statement a 1.5 kg pendulum bob swings in a vertical circle at the end of a 2m long string with negligible weight. If the bob is dropped from a height in which the string is horizontal and taut, what is the angular momentum at the bob's lowest point (in kgm/s^2)? a 40 b 10 c 30...
  43. M

    Can Pendulum Clocks Work in Motion and Acceleration?

    I hope this is the right place for this kind of question - please forgive me if it isn't. I am wondering about the expected effect of acceleration and/or motion on a pendulum clock. It pertains somewhat to relativity theory, but [to my understanding] it is equally a mechanical engineering...
  44. N

    Inverted pendulum attached to cart, cart on frictionless surface & axes

    Homework Statement As a small verification of a larger problem, I'm trying to determine how the dynamics of an inverted pendulum attached to a frictionless cart would behave. The cart has no input force applied, so all horizontal movements would be due purely to the centrifugal+normal...
  45. S

    Calculating G: Simple Pendulum Experiment, problems?

    I need to experimentally calculate gravity (g) with an extreme precision (+/-0,005). We thought about trying an Atwood Machine but too many problems were related to it so we've decided to switch to an Simple Pendulum (with a very long L). What are the problems related to the Simple Pendulum...
  46. N

    State-space description, nonlinear system, inverted pendulum

    Homework Statement Inverted pendulum on a cart on a frictionless surface, write the state-space description of a nonlinear system. outputs are theta(t), theta'(t), y(t), y'(t). Everything is 2-dimensional. Homework Equations theta(t) is the angle between the gravity vector and pendulum y(t)...
  47. C

    What is the correct formula for finding tension in a pendulum bob on a string?

    A 2 kg pendulum bob on a string that is 3m long is released with a velocity of 1 m/s when the support string makes an angle of 30 degrees with the vertical. What is the tension at the highest point of its motion? The Attempt at a Solution Ok so using Newton's second Law, the equation should...
  48. 2

    How Do You Derive the Equation of Motion for an Inverted Pendulum with Springs?

    Can someone explain how they got the term with the red box I understand the kl/2 but not the sin and cos part **Question** Consider the inverted pedulum connected to two equal springs both with constant k. Springs are undelfected when the mass is in the verticle position. If the rod is of...
  49. J

    Pendulum projectile momentum question

    Homework Statement A 0.010 kg pendulum bob is dropped from a height (h) above its equilibrium position. When the bob reaches its equilibrium position, the string breaks and the bob now acts as a projectile. After the string breaks the bob falls 1.5 m while moving 2.0 m horizontally...
  50. E

    Undamped Pendulum: Amplitude & Energy

    An undamped pendulum of mass m = 10kg, and length L = 5m, is released at time t = 0 with an initial displacement θ(0) = 0.05 radians and an initial angular frequency ω(0) = 0.1 radians/s. I need to calculate the amplitude of the oscillations in radians, and the total energy of the oscillations...
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